Question

Diketahui segitiga ABC siku-siku di C . Jika sinA.sinB=1/3 maka carilah nilai sin(A-B)

Answer 1

Verified answer

Jawab

ABC siku siku  di C
A+B = 90

cos (A + B ) = cos 90
cos A cos B - sin A sin B =  0
cos A cos b = 1/3

cos (A  - B) = cos A cos B  + sin A sin b = 2/3

sin (A - B)= √( 1 -  cos²(A-B)) = √(1 - 2/3²) = √(1 - 4/9)
sin (A - B) = √(5/9) = 1/3 √5
sin A cos B + cos A sin B = 1